236 



related components, when the stereometrical configuration of its atoms 

 possesses only axial symmetry. 



If however the configuration of the molecule be such that it has 

 either axes of the second order, or one or more planes of symmetry, 

 there is no possibility of antipodes occurring ; the case where there 

 exists a symmetry-centre in the chemical molecule is of course also 

 included. 



Properly speaking, only the cases where .a single asymmetric 

 carbon-atom, or more generally: a single plurivalent aymmetric 

 atom, is present in a chemical molecule, fall under the simple idea 

 of Van 't Hoff-Le Bel's theory, because only in such cases 

 is the dissymmetry of the molecule really immediately evident, 

 at least, if we disregard for the moment the highly exceptional and 

 very improbable case of an arrangement which will accidentally 

 appear abnormally symmetrical. When however several asymmetric 

 atoms in the molecule are present, and especially when we have 

 to deal with so-called cyclic compounds, or with such possessing 

 double bonds in their molecules, the symmetry of the stereometrical 

 configuration must be studied carefully, so as to be sure that the 

 conclusions drawn about the eventual occurrence of antipodes are 

 really right. Many erroneous statements on this subject are to be 

 found in works on chemistry; and although the full discussion of this 

 matter cannot be given here, this being properly more the special 

 subject of text-books on stereochemistry, rather than that of the 

 present volume, -- yet it seems desirable to treat some important 

 cases here more in detail, because of the great significance of these 

 views, and for the purpose of illustrating the general applicability 

 of the doctrine of symmetry as developed in the previous chapters, 

 to problems of the kind just mentioned also. 



18. Before recapitulating these, it is perhaps better first to 

 make a few remarks on the optical activity of carbon-compounds 

 which possess only one asymmetric carbon-atom. 



The theory of Van 't Hoff and Le Bel has been tested experi- 

 mentally in a great number of cases, and its correctness has really 

 been fully confirmed. 



In all the compounds investigated, the asymmetric carbon-atom 

 was always linked to at least one other carbon-atom; and the 

 question may arise whether the conclusions drawn from that theory 

 will also be valid in cases in which no other carbon-atoms whatever 

 are linked directly to the asymmetric one? 



